1
GATE ECE 2015 Set 3
+2
-0.6
Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ± 2j. Which one of the following statements is TRUE for the signal x=$$\left[ n \right]$$ ?
A
It is a finite duration signal.
B
It is a causal signal.
C
It is a non-causal signal.
D
It is a periodic signal.
2
GATE ECE 2015 Set 1
+2
-0.6
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is ℎ[n]. If ℎ[0] =1, we can conclude.
A
h (n) is real for all n.
B
h (n) is purely imaginary for all n.
C
h (n) is real for only even n.
D
h (n) is purely imaginary for only odd n ݊
3
GATE ECE 2015 Set 1
+2
-0.6
For the discrete-time system shown in the figure, the poles of the system transfer function are located at
A
2, 3
B
1/2, 3
C
1/2 , 1/3
D
2, 1/3
4
GATE ECE 2014 Set 3
Numerical
+2
-0
The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with the region of convergence $$\left| z \right| > 2$$. Then, $$x\left[ 2 \right]$$ is ____________________.